1. Field of the Invention
The present invention relates to electronic circuitry and devices, and particularly to a memristor circuit and a memristor-based emulator for use in digital modulation.
2. Description of the Related Art
Since its inception many proposals and attempts have been reported on using a memristor in digital signal processing (DSP) circuits. Memristor-based DSP applications are mainly focusing on improving the performance of memories and in realizing synapses in neural networks. In most of the reported applications the verification of the DSP circuits is made using mathematical-based memristor models, for example.
A memristor can be considered a basic two-terminal element in electrical circuits that can directly relate a charge flow of electrons with a flux linkage. Therefore, the memristor can be considered as a resistor that changes as a flow of charges flows through it. Specifically, for a memristor, the change that occurs as the charges flow through the memristor does not revert to its original state when the power supply that is applied has been removed. Therefore, the memristor can be considered as having a memory property.
As more charge flows through terminals of the memristor, a state of the memristor will change to another value of resistance bounded by limits RON-ROFF. ROFF can represent a region with a relatively lower dopant concentration, which can indicate there is a relatively lower conductance. RON can represent a region with a relatively higher dopant concentration, which can indicate there is a relatively higher conductance. If a reverse flow of charges are passed through the memristor, the memristor can revert to the previous state. This memory property relates the memristance with a time variable, as well. Relatively important characteristics of the memristor can be the passivity of the memristor, the lack of a discharge of energy which can give the memristor a non-volatile property working as a memory, symmetry in the voltage-current (V-I) characterization curve, a frequency effect on a difference between the RON and ROFF limits, and a difference between applying a small AC signal and a large AC signal.
Different circuit memristor emulator models have been proposed for emulating a memristor or a memristive device. For example, one proposed circuit memristor emulator model uses a large number of active and passive elements; namely two operational amplifiers, four diodes, two Zener diodes, and several bipolar and junction gate field-effect transistor (JFET) transistors in addition to a large number of resistors and capacitors. This type of proposed circuit memristor emulator model typically requires a significant amount of components, as can make it less practical and cost prohibitive. Another proposed circuit memristor emulator model is a coupled variable resistor model, such as a Simulation Program with Integrated Circuit Emphasis (SPICE) model. This proposed circuit memristor emulator model is based on using controlled voltage and current sources available in SPICE. Therefore, by implementing the SPICE model, this proposed circuit memristor emulator model is typically suitable for computer aided simulation, but typically not for use in hardware practical experimentation and testing of memristor-based circuits, for example. Another proposed circuit memristor emulator model is a charge controlled memristor model in a SPICE implementation, for example.
Similarly, another proposed circuit memristor emulator model emulator model consists of a set of analytical equations that can be relatively easily implemented by a Verilog-A language for circuit design and can be relatively easily embedded in SPICE-based simulators. Another proposed circuit memristor emulator model uses a digital potentiometer, an analog-to-digital converter and a microcontroller. Another proposed circuit memristor emulator model is an analog emulator that uses five operational amplifiers, one of them with stringent conditions, a JFET, a floating capacitor and a large number of resistors. In this proposed circuit memristor emulator model, the JFET provides the nonlinear load resistance. The drawbacks with using this proposed circuit memristor emulator model relate to its relative complexity and it is not typically suitable for use as a two terminal device in relatively more complicated circuits. Another example of a proposed circuit memristor emulator model involves a light emitting diode (LED) to provide the nonlinearity, two current-feedback operational amplifiers (CFOAs) and one voltage-feedback operational amplifier (OA), two grounded capacitors and two resistors with one of two resistors floating.
Other implementations of proposed circuit memristor emulator models involve using three or four CFOAs and a number of resistors and capacitors. Moreover, rather than using the commercially available integrated circuit CFOAs, proposed circuit memristor emulator models can be realized using micro-power operational amplifiers. Another proposed circuit memristor emulator model uses three operational amplifiers, one floating capacitor, a large number of resistors, and a light dependent resistor (LDR) and optocoupler to provide the nonlinear load. Another proposed circuit memristor emulator model involves both incremental and decremental memristors. The memristor emulator uses five operational amplifiers, one grounded capacitor, an analog multiplier, a large number of resistors and metal-oxide-semiconductor field-effect transistor (MOSFET) transistors; mostly working as current mirrors, and an analog multiplier, for example.
Another proposed circuit memristor emulator model is a nonlinear resistor that can be transformed into a memristor using a plus-type second-generation current-conveyor (CCII+) and a minus-type current-follower (CF−), a capacitor, an inductor and a nonlinear load resistance; built using a diode and two resistors. Another proposed circuit memristor emulator model includes two operational amplifiers, a floating capacitor, a relatively large number of resistors, and an analog multiplier. Another proposed circuit memristor emulator model uses two analog multipliers, one operational amplifier, an integrator and a number of resistors. Another proposed circuit memristor emulator model uses analog-to-digital, digital-to-analog converters and a microcontroller unit in addition to analog controlled voltage/current sources.
Therefore, the above mentioned proposed circuit memristor emulator models appear to likely have one or more drawbacks. For example, the above mentioned proposed circuit memristor emulator models can be rather complex, either using a large number of active and passive components, or a combination of analog and digital integrated circuits or they can require stringent matching conditions. Another example of a drawback is that the proposed circuit memristor emulator model may be suitable only for computer-aided simulation and typically cannot be used for hardware implementation and experimental testing. Another example of a drawback is that the proposed circuit memristor emulator models may not be suitable for integration into more complicated circuits.
Another example of a drawback is that various of the proposed circuit memristor emulator models use floating capacitors and/or resistors, which may not be suitable for on-chip integration and further may not be easy to minimize the effect of any parasitic capacitors and resistors in a discrete implementation. Another example of a drawback is if the proposed circuit memristor emulator models use an inductor, such inductor use may not be suitable for integration into relatively more complicated circuits. Another example of a drawback is that if the proposed circuit memristor emulator model has a relatively large input impedance, such relatively large impedance can make it suitable for being driven by a voltage but not for being driven by a current.
Therefore, it is desirable for a memristor-based emulator to have a relatively lesser amount of active and passive components and to not require stringent matching conditions. Also, it is desirable for a memristor-based emulator that can be used for hardware implementation and experimental testing, as well as it is desirable for a memristor-based emulator to be suitable for integration into relatively more complicated circuits. Further, it is desirable for a memristor-based emulator to be suitable for on-chip integration, as well as having the ability to minimize the effect of parasitic capacitors and resistors in discrete implementation. Also, it is desirable for a memristor-based emulator to have a relatively smaller input impedance so that it can be driven by a current.
Thus, a memristor-based emulator for use in digital modulation addressing the aforementioned problems is desired.